William Boggs
2021-12-19
Durst37
Beginner2021-12-20Added 37 answers
The easier part is the rotation by two digits: If the minutes are less than 24, this results in a time that is accurate, which happens in cases.
The ones of the minutes must be between 0 and 2, which is the case in 18 out of 60 minutes, because if we rotate by one to the right, they become the tens of the hours. The ones of the hours become the tens of the minutes, so they must be between 0 and 5, which is the case in 16 out of 24 hours. Thus the number of valid rotations is .
There are 288 additional valid rotations since the number of valid rotations must equal the number of valid rotations if we rotate by one to the right or left. Obviously if we don't rotate at all, all times are valid, so the total is
slightly less than half.
22+64
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